A temporal transport-of-intensity equation is derived to describe the evolution of the instantaneous power of the electric field in a dispersive medium. As its spatial counterpart, which can be used to measure wavefronts using the intensity measured after various amounts of diffraction, the temporal transport-of-intensity equation allows the determination of temporal phase shifts using only intensity measurements in a direct noninterferometric way. The application to the characterization of nonlinear phase shifts induced by self-phase modulation and cross-phase modulation is used to determine the nonlinear coefficient of a highly nonlinear fiber.